djj (06/18/82)
Due to numerous requests (must be a lot of porno-math fans out there!), here
is the version of Pretty Polly Nomial that I have been carrying around since
my undergraduate days at the University of Kansas. It is the only version
that I have seen. I'd be interested in seeing any different versions that
anyone out there may have.
Happy Reading --
Dave Johnson
BTL - Piscataway
(...!pyuxcc!djj)
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Impure Mathematics
Wherein it is related how that paragon of womanly virtue, young
"Polly Nomial" (our heroine) is accosted by that notorious villian "Curly Pi",
and factored (Oh, Horror!).
Once upon a time (1/t) pretty Polly Nomial was strolling across a field
of vectors when she came to the boundary of a singularly large matrix. Now
Polly was convergent, and her mother had made it an absolute condition that
she must never enter such an array without her brackets on. Polly, however,
who had changed her variables that morning and was feeling particularly
badly behaved, ignored this condition on the basis that it was insufficient,
and made her way in amongst the complex elements. Rows and columns closed
in on her from all sides. Tangents approached her surface. She became
tensor and tensor. Quite suddenly, two branches of a hyperbola touched her
at a single point. She oscillated violently, lost all sense of directrix,
and went completely divergent. As she reached a turning point, she tripped
over a square root that was protruding from the erf and plunged headlong
down a steep gradient. When she rounded off once more, she found herself
inverted, apparently alone, in a non-Euclidean space.
She was being watched, however. That smooth operator, Curly Pi, was
lurking innerproduct. As his eyes devoured her curvilinear coordinates,
a singular expression crossed his face. He wondered, was she still
convergent? He decided to integrate improperly at once.
Hearing a common fraction behind her, Polly rotated and saw Curly Pi
approaching with his power series extrapolated. She could see at once by
his degenerate conic and dissipative terms that he was bent on no good.
"Arcsinh," she gasped.
"Ho, Ho," he said. "What a symmetric little asymptote you have. I
can see you angles have a lot of secs."
"Oh, sir," she protested, "keep away from me. I haven't got my
brackets on."
"Calm yourself, my dear," said our suave operator. "Your fears are
purely imaginary."
"I,i," she thought. "Perhaps he's not normal but homologous."
"What order are you?" the brute demanded.
"Seventeen," replied Polly.
"I suppose you've never been operated on," leered Curly.
"Of course not," Polly replied quite properly. "I'm absolutely
convergent."
"Come, come," said Curly. "Let's be off to a decimal place I know and
I'll take you to the limits."
"Never," gasped Polly.
"Abscissa," he swore, using the vilest oath he knew. His patience was
gone. Coshing her over the coefficient with a log until she was powerless,
Curly removed her discontinuities. He stared at her significant places, and
began smoothing out her points of inflection. Poor Polly. The algorithmic
method was now her only hope. She felt his hand tending to her asymptotic
limit. Her convergence would soon be gone forever.
There was no mercy, for Curly was a Heavyside operator. Curly's
radius squared itself; Polly's loci quivered. He integrated by parts.
He integrated by partial fractions. After he cofactored, he performed
Runge-Kitta on her. The complex beast even went all the way around and did
a contour integration. Curly went on operating until he had satisfied her
hypothesis; he then exponentiated and became completely orthogonal.
When Polly got home that night, her mother noticed that she was no
longer piecewise continuous, but had been truncated in several places.
It was too late to differentiate now. As the months went by, Polly's
denominator increased monotonically. Finally, she went to l'Hopital
and generated a small but pathological function which left surds all
over the place and drove Polly to Deviation.
The moral of our sad story is:
If you want to keep your expressions convergent,
never allow them a single degree of freedom.